com.numericalmethod.suanshu.optimization.unconstrained.conjugatedirection
Class Powell

java.lang.Object
  com.numericalmethod.suanshu.optimization.unconstrained.steepestdescent.SteepestDescent
      com.numericalmethod.suanshu.optimization.unconstrained.conjugatedirection.Powell

All Implemented Interfaces:

Minimizer, UnconstrainedMinimizer

public class Powell
extends SteepestDescent

Powell's algorithm, starting from an initial point, performs a series of line searches in one iteration. The search directions, except the last one, are all linearly independent.

The major advantage of Powell’s algorithm is that the Hessian needs not be supplied, stored or manipulated.

This algorithm has a few drawbacks and is superseded by Zangwill’s algorithm. For example, in an iteration, linear dependence can sometimes arise, which may fail to find complete set of linearly independent directions that span Eⁿ, even in the case of a convex quadratic problem.

A conjugate direction optimization method is performed by using sequential search directions that bear a strict mathematical relationship to one another.

See Also:

"Theorem 6.5, Algorithm 6.4. Practical Optimization: Algorithms and Engineering Applications. Andreas Antoniou, Wu-Sheng Lu."

Nested Class Summary

Nested classes/interfaces inherited from class com.numericalmethod.suanshu.optimization.unconstrained.steepestdescent.SteepestDescent

SteepestDescent.LineSearch

Field Summary

Fields inherited from class com.numericalmethod.suanshu.optimization.unconstrained.steepestdescent.SteepestDescent

f, g, tol

Constructor Summary

Powell()

Method Summary

protected SteepestDescent.LineSearch

getLineSearch()

Methods inherited from class com.numericalmethod.suanshu.optimization.unconstrained.steepestdescent.SteepestDescent

minimum, search, solve, solve, solve

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Powell

public Powell()

Method Detail

getLineSearch

protected SteepestDescent.LineSearch getLineSearch()

Specified by:

getLineSearch in class SteepestDescent